Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonic trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported ag 'less than': the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test. This paper is not subject to U.S. Similarly, the presence of values reported as less than the limit of detection presents no problems for the first of the three techniques.Meaningful interpretation of the results of these analyses depends on the data collection practices. These techniques are only appropriate for data collected by systematic sampling at a monthly frequency, although stratified random sampling data (with monthly strata) would also be suitable. If the results are to be interpreted as applying to the entire cross section at the station, the water sample must be vertically and horizontally integrated. It is also most important that consistent field and laboratory procedures be used at all times. The achievement of this goal depends on documentation of procedures, training of personnel, and a vigorous program of quality assurance in all phases of the data collection process. Another highly desirable feature is the collection of ancillary data such as time of day, water temperature, and discharge at the time of sample collection. These data provide a basis for explaining a portion of the observed variation in the concentration data. This can enable the analyst to distinguish effects of drought or storms, weather conditions, or effects of solar...

Statistical tests for monotonic trend in seasonal (e.g., monthly) hydrologic time series are commonly confounded by some of the following problems: nonnormal data, missing values, seasonality, censoring (detection limits), and serial dependence. An extension of the Mann-Kendall test for trend (designed for such data) is presented here. Because the test is based entirely on ranks, it is robust against nonnormality and censoring. Seasonality and missing values present no theoretical or computational obstacles to its application. Monte Carlo experiments show that, in terms of type I error, it is robust against serial correlation except when the data have strong long-term persistence (e.g., ARMA (1, 1) monthly processes with 4• > 0.6) or short records (~ 5 years). When there is no serial correlation, it is less powerful than a related simpler test which is not robust against serial correlation.

A set of statistical methods particularly well suited for evaluating time series of monthly water-quality data are presented. The Seasonal Kendall Test for trend is defined. It is a nonparametric test based on the differences between observations in the same month of different years. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation) it is robust by comparison with the parametric alternative of regression. The Seasonal Kendall Slope Estimator, a measure of trend magnitude, is defined. It is closely related to the Seasonal Kendall Test. It is an unbiased estimator of the slope of a linear trend and in comparison to linear regression has a considerably greater precision when the data are log-normally distributed but a moderately lesser precision when the data are normal. The flow-adjusted concentration is defined as the residual (actual minus the conditional expectation) concentration, based on some regression model of concentration as a function of river discharge. By testing these flow-adjusted concentration values for trend over time, one avoids the problem of identifying trends that are artifacts of the sequence of discharges observed. Rather, one is testing for changes in the relationship between concentration and discharge.

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This work has come to fruition under the U.S. Geological Survey (USGS) Global Change Hydrology Program. We would like to acknowledge the many people who have assisted in the development of the Hydro-Climatic Data Network (HCDN).This project was carried out in cooperation with the Office of Surface-Water of the USGS Water Resources Division, which provided technical and logistical support as needed throughout the course of the project. We are especially grateful for the assistance of Ernest F. Hubbard, Jr., Assistant Chief of the Office of Surface-Water, whose knowledge of the USGS streamflow gaging program and sustained interest in the HCDN were invaluable to us in the development of the HCDN. We also thank Verne R. Schneider, currently